7.8: General Post-Tonal Resources - Analyzing 12-Tone Music
The pitch material of a strict 12-tone work is entirely (or nearly entirely) derived from a single 12-tone row . A row is an ordered set of the twelve pitch classes of the chromatic scale. Each of the 12 will appear exactly once, and order is paramount.
12-tone rows that can be related to each other by transposition, inversion, and/or retrograde operations are considered to be forms of the same row. Unless a row has certain properties that allow it to map onto itself when transposed, inverted, or retrograded, there will be 48 forms of the row: prime ( P ), inversion ( I ), retrograde ( R ), and retrograde inversion ( RI ) forms, transposed to begin on each of the 12 pitch classes.
Prime form
The prime form of the row is the main form to which all other forms are referenced. In some pieces, one form of the row will clearly dominate the texture. If that is not the case, choose the most salient row at the beginning of the work and label it P . If more than one row seem equally salient at the beginning, flip a coin. The decision of which to call “prime” is not always important, but the analysis of the piece depends on a single row form serving as a point of reference.
Any row form that is the same as, or a strict transposition of, that opening prime form is also a prime form. Once you have labeled the main prime form at the beginning of the piece, any subsequent row that is an exact transposition of that row is prime. Likewise, any row that exhibits the same succession of pitch-class intervals is also a prime form.
Since P can be transposed to any pitch-class level, we distinguish them with subscripts. There are multiple common systems for deciding the numbering. The simplest, which we will follow in this course, is to number the row by its starting pitch class. If the prime form begins on G (7), it is P 7 ; on B (11), P 11 .
Retrograde form
A retrograde form of the row takes a prime form and exactly reverses the pitch classes. Its interval content, then, are the reverse of the prime forms. Retrograde forms are labeled R followed by a subscript denoting the last pitch class in the row. This will ensure that if two row forms are exact retrogrades of each other, they will have the same subscript.
For example, if a row has the exact reverse interval structure of the prime forms and ends on F-sharp (6), it is R 6 , regardless of its first pitch.
Inversion form
A row form that exactly inverts the interval structure of the prime form (for example, 3 semitones up becomes 3 semitones down—or 9 semitones up, modulo12) is in inversion form. Inversion forms are labeled according to the first pitch class of the row form. An inversion-form row that begins on E-flat (3) is I 3 .
This label is not always the same as the inversion operation that produces it. (See the Analyzing atonal music resource.) If you begin with P 0 , the inversion operation and the resulting row form will have the same subscript. Otherwise, they will be different. Take care not to confuse them.
Retrograde inversion
The relationship of retrograde inversion ( RI ) and inversion ( I ) forms is the same as that between retrograde ( R ) and prime ( P ). Retrograde inversion forms reverse the pitch classes of inversion forms and are named for the last pitch class in the row form.
Interval progressions
Once you have determined (or decided) which row is prime , analyze its interval content in ordered pitch-class intervals . This will help you determine if subsequent row forms are P , I , R , or RI (or if they do not belong to the same row family).
For example, the row for Schoenberg’s Op. 25 is:
[E, F, G, Db, Gb, Eb, Ab, D, B, C, A, Bb].
Its intervals (ascending pitch-class intervals, modulo12) are:
1, 2, 6, 5, 9, 5, 6, 9, 1, 9, 1
(Notice that while no pitch class repeats in the row, several intervals appear more than once.)
The intervals of the inversion form of the row are the same size, opposite direction. You can calculate them by subtracting each of the prime-form intervals from 12:
11, 10, 6, 7, 3, 7, 6, 3, 11, 3, 11
Retrograde intervals are tricky (at first). Reversing pitch classes
changes the direction of each interval
. Thus C–A (9) becomes A–C (3). Thus to get the interval progression of the retrograde forms, reverse the intervals of the
inversion
:
11, 3, 11, 3, 6, 7, 3, 7, 6, 10, 11
(Test this out with the retrograde form of the row: Bb, A, C, B, . . .)
To get the interval succession of the retrograde forms, invert the retrograde interval progression, or reverse the prime interval progression:
1, 9, 1, 9, 6, 5, 9, 5, 6, 2, 1
Take care in determining these first, and it will be easy to classify row forms as you go through a piece. Its interval progression will tell you the type, and the pitch class of the first or last note will give you the subscript. That subscript will tell you the transposition relationship between it and the other row forms of the same type.


6.3: Conductivity
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Conductivity is one of the three primary “constitutive parameters” that is commonly used to characterize the electromagnetic properties of materials (Section 2.8). The key idea is this:
Conductivity is a property of materials that determines conduction current density in response to an applied electric field.
Recall that conduction current is the flow of charge in response to an electric field (Section 6.1). Although the associated force is straightforward to calculate (e.g., Section 5.1), the result is merely the force applied, not the speed at which charge moves in response. The latter is determined by the mobility of charge , which is in turn determined by the atomic and molecular structure of the material. Conductivity relates current density to the applied field directly, without requiring one to grapple separately with the issues of applied force and charge mobility.
In the absence of material – that is, in a true, perfect vacuum – conductivity is zero because there is no charge available to form current, and therefore the current is zero no matter what electric field is applied. At the other extreme, a good conductor is a material that contains a supply of charge that is able to move freely within the material. When an electric field is applied to a good conductor, charge-bearing material constituents move in the direction determined by the electric field, creating current flow in that direction. This relationship is summarized by Ohm’s Law for Electromagnetics :
\[\boxed{ {\bf J} = \sigma {\bf E} } \label{m0010_eMatOhmsLaw} \]
where \({\bf E}\) is electric field intensity (V/m); \({\bf J}\) is the volume current density, a vector describing the current flow, having units of A/m\(^2\) (see Section 6.2); and \(\sigma\) is conductivity. Since \({\bf E}\) has units of V/m, we see \(\sigma\) has units of \(\Omega^{-1}\mbox{m}^{-1}\), which is more commonly expressed as S/m, where 1 S (“siemens”) is defined as \(1~\Omega^{-1}\). Section A3 provides values of conductivity for a representative set of materials.
Conductivity \(\sigma\) is expressed in units of S/m, where 1 S \(=\) 1 \(\Omega^{-1}\).
It is important to note that the current being addressed here is conduction current , and not convection current, displacement current, or some other form of current – see Section 6.2 for elaboration. Summarizing:
Ohm’s Law for Electromagnetics (Equation \ref{m0010_eMatOhmsLaw}) states that volume density of conduction current (A/m\(^2\)) equals conductivity (S/m) times electric field intensity (V/m).
The reader is likely aware that there is also an “Ohm’s Law” in electric circuit theory, which states that current \(I\) (units of A) is voltage \(V\) (units of V) divided by resistance \(R\) (units of \(\Omega\)); i.e., \(I=V/R\). This is in fact a special case of Equation \ref{m0010_eMatOhmsLaw}; see Section 6.4 for more about this.
As mentioned above, \(\sigma\) depends on both the availability and mobility of charge within the material. At the two extremes, we have perfect insulators , for which \(\sigma=0\), and perfect conductors , for which \(\sigma \to \infty\). Some materials approach these extremes, whereas others fall midway between these conditions. Here are a few classes of materials that are frequently encountered:
- A perfect vacuum – “free space” – contains no charge and therefore is a perfect insulator with \(\sigma=0\).
- Good insulators typically have conductivities \(\ll 10^{-10}\) S/m, which is sufficiently low that the resulting currents can usually be ignored. The most important example is air, which has a conductivity only slightly greater than that of free space. An important class of good insulators is lossless dielectrics , 1 which are well-characterized in terms of permittivity (\(\epsilon\)) alone, and for which \(\mu=\mu_0\) and \(\sigma=0\) may usually be assumed.
- Poor insulators have conductivities that are low, but nevertheless sufficiently high that the resulting currents cannot be ignored. For example, the dielectric material that is used to separate the conductors in a transmission line must be considered a poor insulator as opposed to a good (effectively lossless) insulator in order to characterize loss per length along the transmission line, which can be significant. 2 These lossy dielectrics are well-characterized in terms of \(\epsilon\) and \(\sigma\), and typically \(\mu=\mu_0\) can be assumed.
- Semiconductors such as those materials used in integrated circuits have intermediate conductivities, typically in the range \(10^{-4}\) to \(10^{+1}\) S/m.
- Good conductors are materials with very high conductivities, typically greater than \(10^5\) S/m. An important category of good conductors includes metals, with certain metals including alloys of aluminum, copper, and gold reaching conductivities on the order of \(10^8\) S/m. In such materials, minuscule electric fields give rise to large currents. There is no significant storage of energy in such materials, and so the concept of permittivity is not relevant for good conductors.
The reader should take care to note that terms such as good conductor and poor insulator are qualitative and subject to context. What may be considered a “good insulator” in one application may be considered to be a “poor insulator” in another.
One relevant category of material was not included in the above list – namely, perfect conductors . A perfect conductor is a material in which \(\sigma\to\infty\). It is tempting to interpret this as meaning that any electric field gives rise to infinite current density; however, this is not plausible even in the ideal limit. Instead, this condition is interpreted as meaning that \({\bf E}={\bf J}/\sigma\to 0\) throughout the material; i.e., \({\bf E}\) is zero independently of any current flow in the material. An important consequence is that the potential field \(V\) is equal to a constant value throughout the material. (Recall \({\bf E}=-\nabla V\) (Section 5.14), so constant \(V\) means \({\bf E}=0\).) We refer to the volume occupied by such a material as an equipotential volume . This concept is useful as an approximation of the behavior of good conductors; for example, metals are often modeled as perfectly-conducting equipotential volumes in order to simplify analysis.
A perfect conductor is a material for which \(\sigma\to\infty\), \({\bf E}\to 0\), and subsequently \(V\) (the electric potential) is constant.
One final note: It is important to remain aware of the assumptions we have made about materials in this book, which are summarized in Section 2.8. In particular, we continue to assume that materials are linear unless otherwise indicated. For example, whereas air is normally considered to be a good insulator and therefore a poor conductor, anyone who has ever witnessed lightning has seen a demonstration that under the right conditions – i.e., sufficiently large potential difference between earth and sky – current will readily flow through air. This particular situation is known as dielectric breakdown (see Section 5.21). The non-linearity of materials can become evident before reaching the point of dielectric breakdown, so one must be careful to consider this possibility when dealing with strong electric fields.


6.5: Introduction to Basic Formatting and Layout
What you’ll learn to do: change formatting, layout, and styles in Excel.
Like any Microsoft program, Excel will default to certain fonts, texts, and styles when you create a new worksheet. It is also very easy within Excel to format individual cells with cell styles or multiple cells with a table style. Not only can formatting help make your tables more attractive, but it can also help indicate information about the contents, such as whether the data in a cell reaches a target goal. In this section, we will address how to change several default styles within Excel.
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- Introduction to Basic Formatting and Layout. Authored by : Shelli Carter. License : CC BY: Attribution


10.2: Lateralization of Language
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Although functional lateralization studies and analyses find individual differences in personality or cognitive style don't favor one hemisphere or the other, some brain functions occur in one or the other side of the brain. Language tends to be on the left and attention on the right (Nielson, Zielinski, Ferguson, Lainhart & Anderson, 2013 ). There is a lot of evidence that each brain hemisphere has its own distinct functions in language comprehension. Most often, the right hemisphere is referred to as the non-dominant hemisphere and the left is seen as the dominant hemisphere. This distinction is called lateralization (from the Latin word lateral, meaning sidewise) and reason for it first was raised by experiments with split-brain patients. Following a top-down approach we will then discuss the right hemisphere which might have the mayor role in higher level comprehension, but is not quite well understood. Much research has been done on the left hemisphere and we will discuss why it might be dominant before the following sections discuss the fairly well understood fundamental processing of language in this hemisphere of the brain.
Functional asymmetry
Anatomical differences between left and right hemisphere
Initially we will consider the most apparent part of a differentiation between left and right hemisphere: Their differences in shape and structure. As visible to the naked eye there exists a clear asymmetry between the two halves of the human brain: The right hemisphere typically has a bigger, wider and farther extended frontal region than the left hemisphere, whereas the left hemisphere is bigger, wider and extends farther in it’s occipital region (M. T. Banich,"Neuropsychology", ch.3, pg.92). Significantly larger on the left side in most human brains is a certain part of the temporal lobe’s surface, which is called the planum temporale. It is localized near Wernicke’s area and other auditory association areas, wherefore we can already speculate that the left hemisphere might be stronger involved in processes of language and speech treatment.
In fact such a left laterality of language functions is evident in 97% of the population (D. Purves, "Neuroscience", ch.26, pg.649). But actually the percentage of human brains, in which a "left-dominance" of the planum temporale is traceable, is only 67% (D. Purves, "Neuroscience", ch.26, pg.648). Which other factors play aunsolved yet.
Evidence for functional asymmetry from "split brain" patients
In hard cases of epilepsy a rarely performed but popular surgical method to reduce the frequency of epileptic seizures is the so-called corpus callosotomy. Here a radical cut through the connecting "communication bridge" between right and left hemisphere, the corpus callosum, is done; the result is a "split-brain". For patients whose corpus callosum is cut, the risk of accidental physical injury is mitigated, but the side-effect is striking: Due to this eradicative transection of left and right half of the brain these two are not longer able to communicate adequately. This situation provides the opportunity to study differentiation of functionality between the hemispheres. First experiments with split-brain patients were performed by Roger Sperry and his colleagues at the California Institute of Technology in 1960 and 1970 (D. Purves, "Neuroscience", ch.26, pg.646). They lead researchers to sweeping conclusions about laterality of speech and the organization of the human brain in general.
A digression on the laterality of the visual system
Visual system
A visual stimulus, located within the left visual field, projects onto the nasal (inner) part of the left eye’s retina and onto the temporal (outer) part of the right eye’s retina. Images on the temporal retinal region are processed in the visual cortex of the same side of the brain (ipsilateral), whereas nasal retinal information is mapped onto the opposite half of the brain (contralateral).
The stimulus within the left visual field will completely arrive in the right visual cortex to be processed and worked up. In "healthy" brains this information furthermore attains the left hemisphere via the corpus callosum and can be integrated there. In split-brain patients this current of signals is interrupted; the stimulus remains "invisible" for the left hemisphere.
Split Brain Experiments
The experiment we consider now is based on the laterality of the visual system: What is seen in the left half of the visual field will be processed in the right hemisphere and vice versa. Aware of this principle a test operator presents the picture of an object to one half of the visual field while the participant is instructed to name the seen object, and to blindly pick it out of an amount of concrete objects with the contralateral hand.
It can be shown that a picture, for example the drawing of a die, which has only been presented to the left hemisphere, can be named by the participant ("I saw a die"), but is not selectable with the right hand (no idea which object to choose from the table). Contrarily the participant is unable to name the die, if it was recognized in the right hemisphere, but easily picks it out of the heap of objects on the table with the help of the left hand.
These outcomes are clear evidence of the human brain’s functional asymmetry. The left hemisphere seems to dominate functions of speech and language processing, but is unable to handle spatial tasks like vision-independent object recognition. The right hemisphere seems to dominate spatial functions, but is unable to process words and meaning independently. In a second experiment evidence arose that a split-brain patient can only follow a written command (like "get up now!"), if it is presented to the left hemisphere. The right hemisphere can only "understand" pictorial instructions.
The following table (D. Purves, "Neuroscience", ch.26, pg.647) gives a rough distinction of functions:
| Left Hemisphere | Right Hemisphere |
|---|---|
|
|
First it is important to keep in mind that these distinctions comprise only functional dominances, no exclusive competences. In cases of unilateral brain damage, often one half of the brain takes over tasks of the other one. Furthermore it should be mentioned that this experiment works only for stimuli presented for less than a second. This is because not only the corpus callosum, but as well some subcortical comissures serve for interhemispheric transfer. In general both can simultaneously contribute to performance, since they use complement roles in processing.
A digression on handedness
An important issue, when exploring the different brain organization, is handedness, which is the tendency to use the left or the right hand to perform activities. Throughout history, left-handers, which only comprise about 10% of the population, have often been considered being something abnormal. They were said to be evil, stubborn, defiant and were, even until the mid 20th century, forced to write with their right hand.
One most commonly accepted idea, as to how handedness affects the hemispheres, is the brain hemisphere division of labour. Since both speaking and handiwork require fine motor skills, the presumption here is that it would be more efficient to have one brain hemisphere do both, rather than having it divided up. Since in most people, the left side of the brain controls speaking, right-handedness predominates. The theory also predicts that left-handed people have a reversed brain division of labour.
In right handers, verbal processing is mostly done in the left hemisphere, whereas visuospatial processing is mostly done in the opposite hemisphere. Therefore, 95% of speech output is controlled by the left brain hemisphere, whereas only 5% of individuals control speech output in their right hemisphere. Left-handers, on the other hand, have a heterogeneous brain organization. Their brain hemisphere is either organized in the same way as right handers, the opposite way, or even such that both hemispheres are used for verbal processing. But usually, in 70% of the cases, speech is controlled by the left-hemisphere, 15% by the right and 15% by either hemisphere. When the average is taken across all types of left-handedness, it appears that left-handers are less lateralized.
After, for example, damage occurs to the left hemisphere, it follows that there is a visuospatial deficit, which is usually more severe in left-handers than in right-handers. Dissimilarities may derive, in part, from differences in brain morphology, which concludes from asymmetries in the planum temporale. Still, it can be assumed that left-handers have less division of labour between their two hemispheres than right-handers do and are more likely to lack neuroanatomical asymmetries.
There have been many theories as to find out why people are left-handed and what its consequences may be. Some people say that left-handers have a shorter life span or higher accident rates or autoimmune disorders. According to the theory of Geschwind and Galaburda, there is a relation to sex hormones, the immune system, and profiles of cognitive abilities that determine, whether a person is left-handed or not. Concludingly, many genetic models have been proposed, yet the causes and consequences still remain a mystery (M.T.Banich, "Neuropsychology", ch.3, pg. 119).
The right hemisphere
The role of the right hemisphere in text comprehension
The experiments with "split-brain" patients and evidence that will be discussed soon suggest that the right hemisphere is usually not (but in some cases, e.g. 15% of left handed people) dominant in language comprehension. What is most often ascribed to the right hemisphere is cognitive functioning. When damage is done to this part of the brain or when temporal regions of the right hemisphere are removed, this can lead to cognitive-communication problems, such as impaired memory, attention problems, and poor reasoning (L. Cherney, 2001). Investigations lead to the conclusion that the right hemisphere processes information in a gestalt and holistic fashion, with a special emphasis on spatial relationships. Here, an advantage arises for differentiating two distinct faces because it examines things in a global manner and it also reacts to lower spatial, and also auditory, frequency. The former point can be undermined with the fact that the right hemisphere is capable of reading most concrete words and can make simple grammatical comparisons (M. T. Banich,“Neuropsychology“, ch.3, pg.97). But in order to function in such a way, there must be some sort of communication between the brain halves.
Prosody - the sound envelope around words
Consider how different the simple statement "She did it again" could be interpreted in the following context taken from Banich: LYNN: Alice is way into this mountain-biking thing. After breaking her arm, you'd think she'd be a little more cautious. But then yesterday, she went out and rode Captain Jack's. That trail is gnarly - narrow with lots of tree roots and rocks. And last night, I heard that she took a bad tumble on her way down. SARA: She did it again Does Sara say that with rising pitch or emphatically and with falling intonation? In the first case she would ask whether Alice has injured herself again. In the other case she asserts something she knows or imagines: That Alice managed to hurt herself a second time. Obviously the sound envelope around words - prosody - does matter.
Reason to belief that recognition of prosodic patterns appears in the right hemisphere arises when you take into account patients that have damage to an anterior region of the right hemisphere. They suffer from aprosodic speech, that is, their utterances are all at the same pitch. They might sound like a robot from the 80ties. There is another phenomena appearing from brain damage: dysprosodic speech. In that case the patient speaks with disordered intonation. This is not due to a right hemisphere lesion, but arises when damage to the left hemisphere is suffered. The explanation is that the left hemisphere gives ill-timed prosodic cues to the right hemisphere, thus proper intonation is affected.
Beyond words: Inference from a neurological point of view
On the word level, the current studies are mostly consistent with each other and with findings from brain lesion studies. But when it comes to the more complex understanding of whole sentences, texts and storylines, the findings are split. According to E. C. Ferstl’s review “The Neuroanatomy of Text Comprehension. What’s the story so far?” (2004), there is evidence for and against right hemisphere regions playing the key role in pragmatics and text comprehension. On the current state of knowledge, we cannot exactly say how and where cognitive functions like building situation models and inferencing work together with “pure” language processes.
As this chapter is concerned with the neurology of language, it should be remarked that patients with right hemisphere damage have difficulties with inferencing.
You might have to reinterpret the sentence until you realize that "small black bug" does not refer to an animal but rather to a spy device. People with damage in the right hemisphere have problems to do so. They have difficulty to follow the thread of a story and to make inferences about what has been said. Furthermore they have a hard time understanding non-literal aspects of sentences like metaphors, so they might be really horrified when they hear that someone was "Crying her eyes out".
The reader is referred to the next chapter for a detailed discussion of Situation Models
The left hemisphere
Further evidence for left hemisphere dominance: The Wada technique
Before concerning concrete functionality of the left hemisphere, further evidence for the dominance of the left hemisphere is provided. Of relevance is the so-called Wada technique, allowing testing which hemisphere is responsible for speech output and usually being used in epilepsy patients during surgery. It is not a brain imaging technique, but simulates a brain lesion. One of the hemispheres is anesthetized by injecting a barbiturate (sodium amobarbital) in one of the patient’s carotid arteries. Then he is asked to name a number of items on cards. When he is not able to do that, despite the fact that he could do it an hour earlier, the concerned hemisphere is said to be the one responsible for speech output. This test must be done twice, for there is a chance that the patient produces speech bilaterally. The probability for that is not very high, in fact, according to Rasmussen & Milner 1997a (as referred to in Banich, p. 293) it occurs only in 15% of the left-handers and none of the right-handers. (It is still unclear where these differences in left-handers’ brains come from.)
That means that in most people, only one hemisphere “produces” speech output – and in 96% of right-handers and 70% of left-handers, it is the left one. The findings of the brain lesion studies about asymmetry were confirmed here: Normally (in healthy right-handers), the left hemisphere controls speech output.
Explanations of left hemisphere dominance
Two theories why the left hemisphere might have special language capacities are still discussed. The first states that dominance of the left hemisphere is due to a specialization for precise temporal control of oral and manual articulators . Here the main argument is that gestures related to a story line are most often made with the right and therefore by the left hemisphere controlled hand whilst other hand movements appear equally often with both hands. The other theory says that the left hemisphere is dominant because it is specialized for linguistic processing and is due to a single patient - a speaker of American Sign Language with a left hemisphere lesion. He could neither produce nor comprehend ASL, but could still communicate by using gestures in non-linguistic domains.
How innate is the organisational structure of the brain?
Not only cases of left-handers but also brain imaging techniques have shown examples of bilateral language processing: According to ERP studies (by Bellugi et al. 1994 and Neville et al. 1993 as cited in E. Dabrowska, "Language, Mind an Brain" 2004, p. 57), people with the Williams’ syndrome (WS) also have no dominant hemisphere for language. WS patients have a lot of physical and mental disorders, but show, compared to their other (poor) cognitive abilities, very good linguistic skills. And these skills do not rely on one dominant hemisphere, but both of them contribute equally. So, whilst the majority of the population has a dominant left hemisphere for language processing there are a variety of exceptions to that dominance. That there are different “organisation possibilities” in individual brains Dabrowska (p. 57) suggests that the organisational structure in the brain could be less innate and fixed as it is commonly thought.


7.2: Words of Wisdom- Learn What You Don’t Want
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Jamie Edwards
Jamie Edwards
For a long time, my plan had always been to be a kindergarten teacher. But when I began my undergraduate degree I fell into that ever-growing pool of college students who changed their major three times before graduation. I was swayed by family members, my peers, and the economy, but I eventually realized that I was investing my education in the wrong areas for the wrong reasons. It shouldn’t just be about salaries and job security. I needed to find that personal attachment.
 College may feel like a free-for-all at times, but the reality is that it’s one of the most defining times of our lives. It should never be squandered. I started to imagine my life beyond college—what I found important and the type of lifestyle I wanted in the end. I started thinking about the classes that I was actually interested in—the ones that I looked forward to each week and arrived early just so I could get a seat up front.
A turning point for me was when I took the advice of a campus mentor and enrolled in a career exploration course. I learned more about myself in that class than I had in my entire three years at college prior to taking it. It showed me that my passion was something I had always thought about but never thought about as a career. In high school, I could sit in the Guidance Office for hours on end. I enjoyed listening to others—hearing and helping people work through their struggles.
I had seen firsthand how detrimental the absence of career classes can be to someone’s future. Through this realization and my participation in my career exploration class, I saw a viable future in the Higher Education Administration field. As I dove deeper, I was opened to an incredible amount of unique and diverse opportunities to work with students. My main approach was to get a taste anything to do with student services: I shadowed a career counselor in a career services office, attended graduate school fairs and informational sessions, discussed the Higher Education Administration Program with several staff at my college, and most importantly, I talked with my internship coordinator (my mentor). From there, I completed an internship in my prospective field, which gave me a wealth of insight and skills that directly related to my future career goals.
From where I sit now—my former personal and professional struggles in tow—I offer up some pieces of advice that were crucial to getting me where I am today. Whether you’re an undecided major who is looking for guidance or a student with a clearly defined career path, I suggest the following:
- Find a mentor —For me, everything began there. Without my mentor, I wouldn’t have done any of the other items I’m about to suggest. Finding the right mentor is crucial. Look for someone who can complement your personality (typically someone who’s the opposite of you). My advice would be to look beyond your direct supervisor for mentorship. It’s important to create an open forum with your mentor, because there may be a conflict of interest as you discuss work issues and other job opportunities. Potential mentors to consider are an instructor on campus, your academic advisor, a professional currently working in your prospective field, someone you admire in your community, or anyone in your network of friends or family that you feel comfortable discussing your future goals with.
- Enroll in a Career Exploration/Planning course, or something similar —Even if you do not see the effects of this course immediately (such as dramatically changing your major), you will notice the impact down the road. Making educated career choices and learning job readiness skills will always pay off in the end. Through my career exploration class, I learned how to relate my personality and values to potential career fields. These self-assessments changed my entire thought process, and I see that influence daily. Beyond changing the way you think, the knowledge you gain about effective job search strategies is invaluable. Learning how to write purposeful résumés and cover letters, finding the right approach to the interview process, and recognizing your strengths and weaknesses are just a few of the benefits you can gain from these types of courses.
- Complete a Job Shadow and/or Informational Interview —No amount of online research is going to give you the same experience as seeing a job at the front line. In a job shadow or an informational interview, you’re able to explore options with no commitment and see how your in-class experience can carry over to a real world setting. Additionally, you’re expanding your professional network by having that personal involvement. You never know how the connections you make might benefit you in the future. My only regret about job shadowing in college is that I didn’t do it sooner.
- Do an Internship —A main source of frustration for recent grads is the inability to secure an entry-level position without experience. “How do I get a job to gain experience when I can’t get a job without experience?” This is how: do an internship or two! Most colleges even have a course where you can obtain credit for doing it! Not only will you earn credits towards graduation, but you’ll gain the necessary experience to put on your résumé and to discuss in future interviews. Having completed four internships throughout my college career, I can’t say they were all great. However, I don’t regret a single one. The first one showed me the type of field I didn’t want to work in. The second confirmed that I was heading in the right direction with my career. My third and fourth internships introduced me to completely different areas of higher education which broadened my knowledge and narrowed my search simultaneously.
My takeaway is that sometimes you have to learn what you don’t want in order to find out what you do want. The more informed you are about career options through real life conversations and experiences, the better prepared you will be for your future and the more confident you will be in your career decisions. Always explore your options because even if you learn you hate it, at least you’re one step closer to finding what you love.
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Foundations of Academic Success: Words of Wisdom. Edited by Thomas Priester. Essay authored by Jamie Edwards. Located at: https://milnepublishing.geneseo.edu/foundations-of-academic-success/chapter/learn-what-you-dont-want/ License: CC BY: Attribution.


6.2: A Graph as a Collection of Lists
Adjacency list representations of graphs take a more vertex-centric approach. There are many possible implementations of adjacency lists. In this section, we present a simple one. At the end of the section, we discuss different possibilities. In an adjacency list representation, the graph \(G=(V,E)\) is represented as an array, \(\mathtt{adj}\), of lists. The list \(\mathtt{adj[i]}\) contains a list of all the vertices adjacent to vertex \(\mathtt{i}\). That is, it contains every index \(\mathtt{j}\) such that \(\mathtt{(i,j)}\in E\).
int n; List<Integer>[] adj; AdjacencyLists(int n0) { n = n0; adj = (List<Integer>[])new List[n]; for (int i = 0; i < n; i++) adj[i] = new ArrayStack<Integer>(Integer.class); }
(An example is shown in Figure \(\PageIndex{1}\).) In this particular implementation, we represent each list in \(\mathtt{adj}\) as an ArrayStack , because we would like constant time access by position. Other options are also possible. Specifically, we could have implemented \(\mathtt{adj}\) as a DLList .
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 2 | 0 | 1 | 5 | 6 | 4 | 8 | 9 | 10 |
| 4 | 2 | 3 | 7 | 5 | 2 | 2 | 3 | 9 | 5 | 6 | 7 |
| 6 | 6 | 8 | 6 | 7 | 11 | 10 | 11 | ||||
| 5 | 9 | 10 | |||||||||
| 4 |
The \(\mathtt{addEdge(i,j)}\) operation just appends the value \(\mathtt{j}\) to the list \(\mathtt{adj[i]}\):
void addEdge(int i, int j) { adj[i].add(j); }
This takes constant time.
The \(\mathtt{removeEdge(i,j)}\) operation searches through the list \(\mathtt{adj[i]}\) until it finds \(\mathtt{j}\) and then removes it:
void removeEdge(int i, int j) { Iterator<Integer> it = adj[i].iterator(); while (it.hasNext()) { if (it.next() == j) { it.remove(); return; } } }
This takes \(O(\deg(\mathtt{i}))\) time, where \(\deg(\mathtt{i})\) (the degree of \(\mathtt{i}\)) counts the number of edges in \(E\) that have \(\mathtt{i}\) as their source.
The \(\mathtt{hasEdge(i,j)}\) operation is similar; it searches through the list \(\mathtt{adj[i]}\) until it finds \(\mathtt{j}\) (and returns true), or reaches the end of the list (and returns false):
boolean hasEdge(int i, int j) { return adj[i].contains(j); }
This also takes \(O(\deg(\mathtt{i}))\) time.
The \(\mathtt{outEdges(i)}\) operation is very simple; it returns the list \(\mathtt{adj[i]}\) :
List<Integer> outEdges(int i) { return adj[i]; }
This clearly takes constant time.
The \(\mathtt{inEdges(i)}\) operation is much more work. It scans over every vertex \(j\) checking if the edge \(\mathtt{(i,j)}\) exists and, if so, adding \(\mathtt{j}\) to the output list:
List<Integer> inEdges(int i) { List<Integer> edges = new ArrayStack<Integer>(Integer.class); for (int j = 0; j < n; j++) if (adj[j].contains(i)) edges.add(j); return edges; }
This operation is very slow. It scans the adjacency list of every vertex, so it takes \(O(\mathtt{n} + \mathtt{m})\) time.
The following theorem summarizes the performance of the above data structure:
Theorem \(\PageIndex{1}\)
The AdjacencyLists data structure implements the Graph interface. An AdjacencyLists supports the operations
- \(\mathtt{addEdge(i,j)}\) in constant time per operation;
- \(\mathtt{removeEdge(i,j)}\) and \(\mathtt{hasEdge(i,j)}\) in \(O(\deg(\mathtt{i}))\) time per operation;
- \(\mathtt{outEdges(i)}\) in constant time per operation; and
- \(\mathtt{inEdges(i)}\) in \(O(\mathtt{n}+\mathtt{m})\) time per operation.
The space used by a AdjacencyLists is \(O(\mathtt{n}+\mathtt{m})\).
As alluded to earlier, there are many different choices to be made when implementing a graph as an adjacency list. Some questions that come up include:
- What type of collection should be used to store each element of \(\mathtt{adj}\)? One could use an array-based list, a linked-list, or even a hashtable.
- Should there be a second adjacency list, \(\mathtt{inadj}\), that stores, for each \(\mathtt{i}\), the list of vertices, \(\mathtt{j}\), such that \(\mathtt{(j,i)}\in E\)? This can greatly reduce the running-time of the \(\mathtt{inEdges(i)}\) operation, but requires slightly more work when adding or removing edges.
- Should the entry for the edge \(\mathtt{(i,j)}\) in \(\mathtt{adj[i]}\) be linked by a reference to the corresponding entry in \(\mathtt{inadj[j]}\)?
- Should edges be first-class objects with their own associated data? In this way, \(\mathtt{adj}\) would contain lists of edges rather than lists of vertices (integers).
Most of these questions come down to a tradeoff between complexity (and space) of implementation and performance features of the implementation.


10.5: Comparing Two Independent Population Proportions
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When conducting a hypothesis test that compares two independent population proportions, the following characteristics should be present:
- The two independent samples are random samples that are independent.
- The number of successes is at least five, and the number of failures is at least five, for each of the samples.
- Growing literature states that the population must be at least ten or even perhaps 20 times the size of the sample. This keeps each population from being over-sampled and causing biased results.
Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance in the sampling. A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the two population proportions.
Like the case of differences in sample means, we construct a sampling distribution for differences in sample proportions: \(\left(p_{A}^{\prime}-p_{B}^{\prime}\right)\) where \(p_{A}^{\prime}=X_{\frac{A}{n_{A}}}\) and \(p_{B}^{\prime}=X_{\frac{B}{n_{B}}}\) are the sample proportions for the two sets of data in question. \(X_A\) and \(X_B\) are the number of successes in each sample group respectively, and \(n_A\) and \(n_B\) are the respective sample sizes from the two groups. Again we go the Central Figure \(\PageIndex{5}\).
Generally, the null hypothesis allows for the test of a difference of a particular value, \(\delta_{0}\), just as we did for the case of differences in means.
\[H_{0} : p_{1}-p_{2}=\delta_{0}\nonumber\]
\[H_{1} : p_{1}-p_{2} \neq \delta_{0}\nonumber\]
Most common, however, is the test that the two proportions are the same. That is,
\[H_{0} : p_{\mathrm{A}}=p_{B}\nonumber\]
\[H_{a} : p_{\mathrm{A}} \neq p_{B}\nonumber\]
To conduct the test, we use a pooled proportion, \(p_c\).
\[\textbf{The pooled proportion is calculated as follows:}\nonumber\]
\[p_{c}=\frac{x_{A}+x_{B}}{n_{A}+n_{B}}\nonumber\]
\[\textbf{The test statistic (z-score) is:}\nonumber\]
\[Z_{c}=\frac{\left(p_{A}^{\prime}-p_{B}^{\prime}\right)-\delta_{0}}{\sqrt{p_{c}\left(1-p_{c}\right)\left(\frac{1}{n_{A}}+\frac{1}{n_{B}}\right)}}\nonumber\]
where \(\delta_{0}\) is the hypothesized differences between the two proportions and p c is the pooled variance from the formula above.
Example \(\PageIndex{1}\)
A bank has recently acquired a new branch and thus has customers in this new territory. They are interested in the default rate in their new territory. They wish to test the hypothesis that the default rate is different from their current customer base. They sample 200 files in area A, their current customers, and find that 20 have defaulted. In area B, the new customers, another sample of 200 files shows 12 have defaulted on their loans. At a 10% level of significance can we say that the default rates are the same or different?
- Answer
-
Solution 10.6
This is a test of proportions. We know this because the underlying random variable is binary, default or not default. Further, we know it is a test of differences in proportions because we have two sample groups, the current customer base and the newly acquired customer base. Let A and B be the subscripts for the two customer groups. Then p A and p B are the two population proportions we wish to test.
Random Variable:
\(P_{A}^{\prime}-P_{B}^{\prime}\) = difference in the proportions of customers who defaulted in the two groups.
\(H_{0} : p_{A}=p_{B}\)
\(H_{a} : p_{A} \neq p_{B}\)
The words "is a difference" tell you the test is two-tailed.
Distribution for the test: Since this is a test of two binomial population proportions, the distribution is normal:
\(p_{c}=\frac{x_{A}+x_{B}}{n_{A}+n_{B}}=\frac{20+12}{200+200}=0.08\) \(1-p_{c}=0.92\)
\(\left(p^{\prime} A-p^{\prime} B\right)=0.04\) follows an approximate normal distribution.
Estimated proportion for group A: \(p^{\prime}_{A}=\frac{x_{A}}{n_{A}}=\frac{20}{200}=0.1\)
Estimated proportion for group B: \(p^{\prime}_{B}=\frac{x_{B}}{n_{B}}=\frac{12}{200}=0.06\)
The estimated difference between the two groups is : \(p_{A}^{\prime}-p_{B}^{\prime}=0.1-0.06=0.04\).
\[Z_{c}=\frac{\left(\mathrm{P}_{A}^{\prime}-\mathrm{P}_{B}^{\prime}\right)-\delta_{0}}{P_{c}\left(1-P_{c}\right)\left(\frac{1}{n_{A}}+\frac{1}{n_{B}}\right)}=0.54\nonumber\]
The calculated test statistic is .54 and is not in the tail of the distribution.
Make a decision: Since the calculate test statistic is not in the tail of the distribution we cannot reject \(H_0\).
Conclusion: At a 1% level of significance, from the sample data, there is not sufficient evidence to conclude that there is a difference between the proportions of customers who defaulted in the two groups.
Try It \(\PageIndex{1}\)
Two types of valves are being tested to determine if there is a difference in pressure tolerances. Fifteen out of a random sample of 100 of Valve A cracked under 4,500 psi. Six out of a random sample of 100 of Valve B cracked under 4,500 psi. Test at a 5% level of significance.


3.E: Microbial Biochemistry (Exercises)
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- Ying Liu
- City College of San Francisco
7.1: Organic Molecules
Biochemistry is the discipline that studies the chemistry of life, and its objective is to explain form and function based on chemical principles. Organic chemistry is the discipline devoted to the study of carbon-based chemistry, which is the foundation for the study of biomolecules and the discipline of biochemistry. Both biochemistry and organic chemistry are based on the concepts of general chemistry.
Multiple Choice
Which of these elements is not a micronutrient?
- C
- Ca
- Co
- Cu
- Answer
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A
Which of the following is the name for molecules whose structures are nonsuperimposable mirror images?
- structural isomers
- monomers
- polymers
- enantiomers
- Answer
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D
True/False
Aldehydes, amides, carboxylic acids, esters, and ketones all contain carbonyl groups.
- Answer
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True
Two molecules containing the same types and numbers of atoms but different bonding sequences are called enantiomers.
- Answer
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False
Short Answer
Why are carbon, nitrogen, oxygen, and hydrogen the most abundant elements in living matter and, therefore, considered macronutrients?
Identify the functional group in each of the depicted structural formulas.
Critical Thinking
The structural formula shown corresponds to penicillin G, a narrow-spectrum antibiotic that is given intravenously or intramuscularly as a treatment for several bacterial diseases. The antibiotic is produced by fungi of the genus Penicillium . (a) Identify three major functional groups in this molecule that each comprise two simpler functional groups. (b) Name the two simpler functional groups composing each of the major functional groups identified in (a).
7.2: Carbohydrates
The most abundant biomolecules on earth are carbohydrates. From a chemical viewpoint, carbohydrates are primarily a combination of carbon and water, and many of them have the empirical formula (CH 2 O) n , where n is the number of repeated units. This view represents these molecules simply as “hydrated” carbon atom chains in which water molecules attach to each carbon atom, leading to the term “carbohydrates.”
Multiple Choice
By definition, carbohydrates contain which elements?
- carbon and hydrogen
- carbon, hydrogen, and nitrogen
- carbon, hydrogen, and oxygen
- carbon and oxygen
- Answer
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C
Monosaccharides may link together to form polysaccharides by forming which type of bond?
- hydrogen
- peptide
- ionic
- glycosidic
- Answer
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D
Matching
Match each polysaccharide with its description.
| ___chitin | A. energy storage polymer in plants |
| ___glycogen | B. structural polymer found in plants |
| ___starch | C. structural polymer found in cell walls of fungi and exoskeletons of some animals |
| ___cellulose | D. energy storage polymer found in animal cells and bacteria |
- Answer
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C, D, A, B
Short Answer
What are monosaccharides, disaccharides, and polysaccharides?
Critical Thinking
The figure depicts the structural formulas of glucose, galactose, and fructose. (a) Circle the functional groups that classify the sugars either an aldose or a ketose, and identify each sugar as one or the other. (b) The chemical formula of these compounds is the same, although the structural formula is different. What are such compounds called?
Structural diagrams for the linear and cyclic forms of a monosaccharide are shown. (a) What is the molecular formula for this monosaccharide? (Count the C, H and O atoms in each to confirm that these two molecules have the same formula, and report this formula.) (b) Identify which hydroxyl group in the linear structure undergoes the ring-forming reaction with the carbonyl group.
The term “dextrose” is commonly used in medical settings when referring to the biologically relevant isomer of the monosaccharide glucose. Explain the logic of this alternative name.
7.3: Lipids
Although they are composed primarily of carbon and hydrogen, lipid molecules may also contain oxygen, nitrogen, sulfur, and phosphorous. Lipids serve numerous and diverse purposes in the structure and functions of organisms. They can be a source of nutrients, a storage form for carbon, energy-storage molecules, or structural components of membranes and hormones. Lipids comprise a broad class of many chemically distinct compounds, the most common of which are discussed in this section.
Multiple Choice
Which of the following describes lipids?
- a source of nutrients for organisms
- energy-storage molecules
- molecules having structural role in membranes
- molecules that are part of hormones and pigments
- all of the above
- Answer
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E
Molecules bearing both polar and nonpolar groups are said to be which of the following?
- hydrophilic
- amphipathic
- hydrophobic
- polyfunctional
- Answer
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B
True/False
Lipids are a naturally occurring group of substances that are not soluble in water but are freely soluble in organic solvents.
- Answer
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False
Fatty acids having no double bonds are called “unsaturated.”
- Answer
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False
A triglyceride is formed by joining three glycerol molecules to a fatty acid backbone in a dehydration reaction.
- Answer
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False
Fill in the Blank
Waxes contain esters formed from long-chain __________ and saturated __________, and they may also contain substituted hydrocarbons.
- Answer
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alcohols; fatty acids
Cholesterol is the most common member of the __________ group, found in animal tissues; it has a tetracyclic carbon ring system with a __________ bond in one of the rings and one free __________group.
- Answer
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steroid; double; hydroxyl
Critical Thinking
Microorganisms can thrive under many different conditions, including high-temperature environments such as hot springs. To function properly, cell membranes have to be in a fluid state. How do you expect the fatty acid content (saturated versus unsaturated) of bacteria living in high-temperature environments might compare with that of bacteria living in more moderate temperatures?
Short Answer
Describe the structure of a typical phospholipid. Are these molecules polar or nonpolar?
7.4: Proteins
Amino acids are capable of bonding together in essentially any number, yielding molecules of essentially any size that possess a wide array of physical and chemical properties and perform numerous functions vital to all organisms. The molecules derived from amino acids can function as structural components of cells and subcellular entities, as sources of nutrients, as atom- and energy-storage reservoirs, and as functional species such as hormones, enzymes, receptors, and transport molecules.
Multiple Choice
Which of the following groups varies among different amino acids?
- hydrogen atom
- carboxyl group
- R group
- amino group
- Answer
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C
The amino acids present in proteins differ in which of the following?
- size
- shape
- side groups
- all of the above
- Answer
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D
Which of the following bonds are not involved in tertiary structure?
- peptide bonds
- ionic bonds
- hydrophobic interactions
- hydrogen bonds
- Answer
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A
Fill in the Blank
The sequence of amino acids in a protein is called its __________.
- Answer
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Primary structure
Denaturation implies the loss of the __________ and __________ structures without the loss of the __________ structure.
- Answer
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secondary, tertiary, primary
True/False
A change in one amino acid in a protein sequence always results in a loss of function.
- Answer
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False
Critical Thinking
Heating a protein sufficiently may cause it to denature. Considering the definition of denaturation, what does this statement say about the strengths of peptide bonds in comparison to hydrogen bonds?
The image shown represents a tetrapeptide. (a) How many peptide bonds are in this molecule? (b) Identify the side groups of the four amino acids composing this peptide.
7.5: Using Biochemistry to Identify Microorganisms
Accurate identification of bacteria is essential in a clinical laboratory for diagnostic and management of epidemics, pandemics, and food poisoning caused by bacterial outbreaks. In this section, we discuss a few methods that use biochemical characteristics to identify microorganisms.
Multiple Choice
Which of the following characteristics/compounds is not considered to be a phenotypic biochemical characteristic used of microbial identification?
- poly-β-hydroxybutyrate
- small-subunit (16S) rRNA gene
- carbon utilization
- lipid composition
- Answer
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B
Proteomic analysis is a methodology that deals with which of the following?
- the analysis of proteins functioning as enzymes within the cell
- analysis of transport proteins in the cell
- the analysis of integral proteins of the cell membrane
- the study of all accumulated proteins of an organism
- Answer
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D
Which method involves the generation of gas phase ions from intact microorganisms?
- FAME
- PLFA
- MALDI-TOF
- Lancefield group testing
- Answer
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C
Which method involves the analysis of membrane-bound carbohydrates?
- FAME
- PLFA
- MALDI-TOF
- Lancefield group testing
- Answer
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D
Which method involves conversion of a microbe’s lipids to volatile compounds for analysis by gas chromatography?
- FAME
- proteomic analysis
- MALDI-TOF
- Lancefield group testing
- Answer
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A
Fill in the Blank
A FAME analysis involves the conversion of _______ to more volatile _____ for analysis using ____________.
- Answer
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fatty acids, methyl esters, gas chromatography
True/False
MALDI-TOF relies on obtaining a unique mass spectrum for the bacteria tested and then checking the acquired mass spectrum against the spectrum databases registered in the analysis software to identify the microorganism.
- Answer
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True
Lancefield group tests can identify microbes using antibodies that specifically bind cell-surface proteins.
- Answer
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False
Short Answer
Compare MALDI-TOF, FAME, and PLFA, and explain how each technique would be used to identify pathogens.


3.5: Crisis and Crisis Intervention
If you were asked to describe someone in crisis, what would come to your mind? Many of us might draw on traditional images of someone anxiously wringing their hands, pacing the halls, having a verbal outburst, or acting erratically. Health care professionals should be aware that crisis can be reflected in these types of behaviors, but it can also be demonstrated in various verbal and nonverbal signs. There are many potential causes of crisis, and there are four phases an individual progresses through to crisis. Nurses and other health care professionals are often the frontline care providers when an individual faces a crisis, so it is important to recognize signs of crisis, know what to assess, intervene appropriately, and evaluate crisis resolution.
Definition of Crisis
A crisis can be broadly defined as the inability to cope or adapt to a stressor. Historically, the first examination of crisis and development of formal crisis intervention models occurred among psychologists in the 1960s and 1970s. Although definitions of crisis have evolved, there are central tenets related to an individual’s stress management.
Consider the historical context of crisis as first formally defined in the literature by Gerald Caplan. Crisis was defined as a situation that produces psychological disequilibrium in an individual and constitutes an important problem in which they can’t escape or solve with their customary problem-solving resources. [1] This definition emphasized the imbalance created by situation stressors.
Albert Roberts updated the concept of crisis management in more recent years to include a reflection on the level of an individual’s dysfunction. He defined crisis as an acute disruption of psychological homeostasis in which one’s usual coping mechanisms fail with evidence of distress and functional impairment. [2] A person’s subjective reaction to a stressful life experience compromises their ability (or inability) to cope or function.
Causes of Crisis
A crisis can emerge for individuals due to a variety of events. It is also important to note that events may be managed differently by different individuals. For example, a stressful stimulus occurring for Patient A may not induce the same crisis response as it does for Patient B. Therefore, nurses must remain vigilant and carefully monitor each patient for signs of emerging crisis.
A crisis commonly occurs when individuals experience some sort of significant life event. These events may be unanticipated, but that is not always the case. An example of anticipated life events that may cause a crisis include the birth of a baby. For example, the birth (although expected) can result in a crisis for some individuals as they struggle to cope with and adapt to this major life change. Predictable, routine schedules from before the child was born are often completely upended. Priorities shift to an unyielding focus on the needs of the new baby. Although many individuals welcome this change and cope effectively with the associated life changes, it can induce crises in those who are unprepared for such a change.
Crisis situations are more commonly associated with unexpected life events. Individuals who experience a newly diagnosed critical or life-altering illness are at risk for experiencing a crisis. For example, a client experiencing a life-threatening myocardial infarction or receiving a new diagnosis of cancer may experience a crisis. Additionally, the crisis may be experienced by family and loved ones of the patient as well. Nurses should be aware that crisis intervention and the need for additional support may occur in these types of situations and often extend beyond the needs of the individual patient.
Other events that may result in crisis development include stressors such as the loss of a job, loss of one’s home, divorce, or death of a loved one. It is important to be aware that clustering of multiple events can also cause stress to build sequentially so that individuals can no longer successfully manage and adapt, resulting in crisis.
Categories of Crises
Due to a variety of stimuli that can cause the emergence of a crisis, crises can be categorized to help nurses and health care providers understand the crisis experience and the resources that may be most beneficial for assisting the client and their family members. Crises can be characterized into one of three categories: maturational, situational, or social crisis. Table 3.5a explains characteristics of the different categories of crises and provides examples of stressors associated with that category.
Table 3.5a Categories of Crises
| Category | Characteristics | Examples |
|---|---|---|
|
Maturational
(also known as Developmental crisis) |
|
|
| Situational |
|
|
|
Social
(also known as Adventitious crisis) |
|
|
Phases of Crisis
The process of crisis development can be described as four distinct phases. The phases progress from initial exposure to the stressor, to tension escalation, to an eventual breaking point. These phases reflect a sequential progression in which resource utilization and intervention are critical for assisting a client in crisis. Table 3.5b describes the various phases of crisis, their defining characteristics, and associated signs and symptoms that individuals may experience as they progress through each phase.
Table 3.5b Crisis Phases [3] , [4]
| Crisis Phase | Defining Characteristics | Signs and Symptoms |
|---|---|---|
|
Phase 1:
Normal Stress & Anxiety |
Exposure to a precipitating stressor.
Stressors may be considered minor annoyances and inconveniences of everyday life. |
Anxiety levels or the stress response begin to elevate.
Individuals try using previously successful problem-solving techniques to attempt resolution of the stressor. Individuals are rational and in control of their behavior and emotions. |
|
Phase 2:
Rising Anxiety Level |
Problem-solving techniques do not relieve the stressor.
Use of past coping strategies are not successful. |
Anxiety levels increase and individuals experience increased discomfort.
Feelings of helplessness, confusion, and disorganized thinking may occur. Individuals may complain of “feeling lost” in how to proceed. Individuals may experience elevated heart rate and respiration rate. Their voice pitch may be higher with a more rapid speech pattern. Nervous habits such as finger or foot tapping may occur. |
|
Phase 3:
Severe Level of Stress and Anxiety |
Individuals use all possible internal and external resources.
Problems are explored from different perspectives, and new problem-solving techniques are attempted. |
Equilibrium may be restored if new problem-solving approaches are successful. Individuals experience decreased anxiety if resolution occurs.
If new problem-solving techniques are not successful, the level of anxiety worsens, and functioning is impaired as the stressor continues to impact the individual. Capacity to reason becomes significantly diminished, and behaviors become more disruptive. Communication processes may include yelling and swearing. Individuals may become very argumentative or use threats. Individuals may pace; clench their fists; perspire heavily; or demonstrate rapid, shallow, panting breaths. |
|
Phase 4:
Crisis |
If resolution is not achieved, tension escalates to a critical breaking point. |
Individuals experience unbearable anxiety, increased feelings of panic, and disordered thinking processes. There is an urgent need to end emotional discomfort. Many cognitive functions are impaired as the crisis event becomes thought consuming. Emotions are labile, and some patients may experience psychotic thinking.
*It is important to note that some individuals at this level of crisis may be a danger to themselves and others. |
Crisis Assessment
Nurses must be aware of the potential impact of stressors for their clients and the ways in which they may manifest in a crisis. The first step in assessing for crisis occurs with the basic establishment of a therapeutic nurse-patient relationship. Understanding who your patient is, what is occurring in their life, what resources are available to them, and their individual beliefs, supports, and general demeanor can help a nurse determine if a patient is at risk for ineffective coping and possible progression to crisis.
Crisis symptoms can manifest in various ways. Nurses should carefully monitor for signs of the progression through the phases of crisis such as the following:
- Escalating anxiety
- Denial
- Confusion or disordered thinking
- Anger and hostility
- Helplessness and withdrawal
- Inefficiency
- Hopelessness and depression
- Steps toward resolution and reorganization
When a nurse identifies these signs in a patient or their family members, it is important to carefully explore the symptoms exhibited and the potential stressors. Collecting information regarding the severity of the stress response, the individual’s or family’s resources, and the crisis phase can help guide the nurse and health care team toward appropriate intervention.
Crisis Interventions
Crisis intervention is an important role for the nurse and health care team to assist patients and families toward crisis resolution. Resources are employed, and interventions are implemented to therapeutically assist the individual in whatever phase of crisis they are experiencing. Depending on the stage of the crisis, various strategies and resources are used.
The goals of crisis intervention are the following:
- Identify, assess, and intervene
- Return the individual to a prior level of functioning as quickly as possible
- Lessen negative impact on future mental health
During the crisis intervention process, new skills and coping strategies are acquired, resulting in change. A crisis state is time-limited, usually lasting several days but no longer than four to six weeks.
Various factors can influence an individual’s ability to resolve a crisis and return to equilibrium, such as realistic perception of an event, adequate situational support, and adequate coping strategies to respond to a problem. Nurses can implement strategies to reinforce these factors.
Strategies for Crisis Phase 1 and 2
Table 3.5c describes strategies and techniques for early phases of a crisis that can help guide the individual toward crisis resolution.
Table 3.5c Phase 1 & 2 Early Crisis Intervention Strategies [5]
| Verbal | Strategies | Examples |
|---|---|---|
| Therapeutic use of words holds significant power to defuse the stress response. | Encourage the person to express their thoughts and concerns. | “I understand how hard this must be for you.” |
| Be attuned to the individual’s tone of voice and body language. | Use a shared problem-solving approach. Avoid being defensive. | “I understand your feelings of frustration. How can we correct this problem?” |
| Be attuned to word choice. | Use empathetic inquiry. | “You seem to be upset. Tell me more about what is bothering you.” |
| Nonverbal | Strategies | Example |
| Be aware of your nonverbal messages and be in control of your body positions. | Be calm and act calm. Invite the client to sit to help them calm down and demonstrate you are calm. | Maintain nonthreatening eye contact, smile, and keep hands open and visible. |
| Listen. | Nod your head to demonstrate that you are engaged with the individual. | |
| Respect personal space. | Maintain distance and avoid touching an individual who is upset. | |
| Approach the patient from an angle or from the side. | Avoid directly approaching an individual, as it can feel confrontational. | |
| Avoid threatening gestures. | Avoid finger pointing or crossing arms. | |
| Demonstrate respect. | Mirror the individual’s nonverbal messaging. Avoid laughing or joking. |
Strategies for Crisis Phase 3
If an individual continues to progress in severity to higher levels of crisis, the previously identified verbal and nonverbal interventions for Phase 1 and Phase 2 may be received with a variability of success. For example, for a receptive individual who is still in relative control of their emotions, the verbal and nonverbal interventions may still be well-received. However, if an individual has progressed to Phase 3 with emotional lability, the nurse must recognize this escalation and take additional measures to protect oneself. If an individual demonstrates loss of problem-solving ability or the loss of control, the nurse must take measures to ensure safety for themselves and others in all interactions with the patient. This can be accomplished by calling security or other staff to assist when engaging with the patient. It is important to always note the location of exits in the patient’s room and ensure the patient is never between the nurse and the exit. Rapid response devices may be worn, and nurses should feel comfortable using them if a situation begins to escalate.
Verbal cues can still hold significant power even in a late phase of crisis. The nurse should provide direct cues to an escalating patient such as, “Mr. Andrews, please sit down and take a few deep breaths. I understand you are angry. You need to gain control of your emotions, or I will have to call security for assistance.” This strategy is an example of limit-setting that can be helpful for de-escalating the situation and defusing tension. Setting limits is important for providing behavioral guidance to a patient who is escalating, but it is very different from making threats. Limit-setting describes the desired behavior whereas making threats is nontherapeutic. See additional examples contrasting limit-setting and making threats in the following box. [6]
Examples of Limit-Setting Versus Making Threats [7]
- Threat: “If you don’t stop, I’m going to call security!”
- Limit-Setting: “Please sit down. I will have to call for assistance if you can’t control your emotions.”
- Threat: “If you keep pushing the call button over and over like that, I won’t help you.”
- Limit-Setting: “Ms. Ferris, I will come as soon as I am able when you need assistance, but please give me a chance to get to your room.”
- Threat: “That type of behavior won’t be tolerated!”
- Limit-Setting: “Mr. Barron, please stop yelling and screaming at me. I am here to help you.”
Strategies for Crisis Phase 4
A person who is experiencing an elevated phase of crisis is not likely to be in control of their emotions, cognitive processes, or behavior. It is important to give them space so they don’t feel trapped. Many times these individuals are not responsive to verbal intervention and are solely focused on their own fear, anger, frustration, or despair. Don’t try to argue or reason with them. Individuals in Phase 4 of crisis often experience physical manifestations such as rapid heart rate, rapid breathing, and pacing.
If you can’t successfully de-escalate an individual who is becoming increasingly more agitated, seek assistance. If you don’t believe there is an immediate danger, call a psychiatrist, psychiatric-mental health nurse specialist, therapist, case manager, social worker, or family physician who is familiar with the person’s history. The professional can assess the situation and provide guidance, such as scheduling an appointment or admitting the person to the hospital. If you can’t reach someone and the situation continues to escalate, consider calling your county mental health crisis unit, crisis response team, or other similar contacts. If the situation is life-threatening or if serious property damage is occurring, call 911 and ask for immediate assistance. When you call 911, tell them someone is experiencing a mental health crisis and explain the nature of the emergency, your relationship to the person in crisis, and whether there are weapons involved. A nurse who assesses a patient in this phase should observe the patient’s behaviors and take measures to ensure the patient and others remain safe. A person who is out of control may require physical or chemical restraints to be safe. Nurses must be aware of organizational policies and procedures, as well as documentation required for implementing restraints, if the patient’s or others’ safety is in jeopardy.
Review guidelines for safe implementation of restraints in the “ Restraints ” section of Open RN Nursing Fundamentals .
Crisis Resources
Depending on the type of stressors and the severity of the crisis experienced, there are a variety of resources that can be offered to patients and their loved ones. Nurses should be aware of community and organizational resources that are available in their practice settings. Support groups, hotlines, shelters, counseling services, and other community resources like the Red Cross may be helpful. Read more about potential national and local resources in the following box.
Mental Health Crisis Resources
NAMI: National Alliance on Mental Health
ADRC of Central Wisconsin
Wisconsin County Crisis Lines
Wisconsin Suicide & Crisis Hotlines
Mental Health Crisis
When an individual is diagnosed with a mental health disorder, the potential for crisis is always present. Risk of suicide is always a priority concern for people with mental health conditions in crisis. Any talk of suicide should always be taken seriously. Most people who attempt suicide have given some warning. If someone has attempted suicide before, the risk is even greater. Read more about assessing suicide risk in the “ Establishing Safety ” section of Chapter 1. Encouraging someone who is having suicidal thoughts to get help is a safety priority.
Common signs that a mental health crisis is developing are as follows:
- Inability to perform daily tasks like bathing, brushing teeth, brushing hair, or changing clothes
- Rapid mood swings, increased energy level, inability to stay still, pacing, suddenly depressed or withdrawn, or suddenly happy or calm after period of depression
- Increased agitation with verbal threats; violent, out-of-control behavior or destruction of property
- Abusive behavior to self and others, including substance misuse or self-harm (cutting)
- Isolation from school, work, family, or friends
- Loss of touch with reality (psychosis) – unable to recognize family or friends, confused, doesn’t understand what people are saying, hearing voices, or seeing things that aren’t there
- Paranoia
Clients with mental illness and their loved ones need information for what to do if they are experiencing a crisis.  It outlines what can contribute to a crisis, warning signs that a crisis is emerging, strategies to help de-escalate a crisis, and available resources.
Read NAMI’s Navigating a Mental Health Crisis: A NAMI Resource Guide for Those Experiencing a Mental Health Emergency .
- Caplan, G. (1964). Principles of preventive psychiatry. Basic Books. ↵
- Roberts, A. R. (2005). Bridging the past and present to the future of crisis intervention and crisis management. In A. R. Roberts (Ed.), Crisis intervention handbook: Assessment, treatment, and research (3rd ed.). Oxford University Press. pp. 3-34. ↵
- Caplan, G. (1964). Principles of preventive psychiatry. Basic Books. ↵
- Centers for Disease Control and Prevention. (2018, May 25). The National Institute for Occupational Health and Safety. https://www.cdc.gov/niosh/ ↵
- Centers for Disease Control and Prevention. (2018, May 25). The National Institute for Occupational Health and Safety. https://www.cdc.gov/niosh/ ↵
- Centers for Disease Control and Prevention. (2018, May 25). The National Institute for Occupational Health and Safety. https://www.cdc.gov/niosh/ ↵
- Centers for Disease Control and Prevention. (2018, May 25). The National Institute for Occupational Health and Safety. https://www.cdc.gov/niosh/ ↵
- Brister, T. (2018). Navigating a mental health crisis: A NAMI resource guide for those experiencing a mental health emergency. National Alliance on Mental Illness. https://www.nami.org/Support-Education/Publications-Reports/Guides/Navigating-a-Mental-Health-Crisis/Navigating-A-Mental-Health-Crisis?utm_source=website&utm_medium=cta&utm_campaign=crisisguide ↵